# Near critical scaling relations for planar Bernoulli percolation without differential inequalities

@inproceedings{DuminilCopin2021NearCS, title={Near critical scaling relations for planar Bernoulli percolation without differential inequalities}, author={Hugo Duminil-Copin and Ioan Manolescu and Vincent Tassion}, year={2021} }

We provide a new proof of the near-critical scaling relation β = ξ1ν for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach that does not invoke Russo’s formula, but rather relates differences in crossing probabilities at different scales. The argument is shorter and more robust than previous ones and is more likely to be adapted to other models. The same approach may be used to prove the other scaling relations appearing in Kesten’s work.

## One Citation

Sharpness of Bernoulli percolation via couplings

- Mathematics
- 2022

In this paper, we consider Bernoulli percolation on a locally finite, transitive and infinite graph (e.g. the hypercubic lattice Z). We prove the following estimate, where θn(p) is the probability…

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